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Numerical Algorithms
Erschienen in: Numerical Algorithms 4/2021

19.10.2020 | Original Paper

Local and parallel finite element methods for the coupled Stokes/Darcy model

verfasst von: Guangzhi Du, Liyun Zuo

Erschienen in: Numerical Algorithms | Ausgabe 4/2021

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Abstract

In this paper, based on two-grid discretizations, two kinds of local and parallel finite element methods are proposed and investigated for the coupled Stokes/Darcy model. Following the idea presented in Xu and Zhou (Math. Comput. 69, 881–909 1999). a classical local and parallel finite element method is proposed and investigated. To derive global continuous approximations, a new local and parallel finite element method is devised by combining the partition of unity. We theoretically analyze the resulting formulations and derive optimal error estimates. Numerical experiments are reported to assess the theoretical results.
Vorheriger Artikel Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants
Nächster Artikel New degrees of freedom for high-order Whitney approximations of Darcy’s flows

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Literatur
1.
Cai, M., Mu, M.: A multilevel decoupled method for a mixed Stokes/Darcy model. J. Comput. Appl. Math. 236, 2452–2465 (2012)MathSciNetCrossRef
2.
Cai, M., Mu, M., Xu, J.: Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach. SIAM J. Numer. Anal. 47, 3325–3338 (2009)MathSciNetCrossRef
3.
Chen, W., Gunzburger, M., Hua, F., Wang, X.: A parallel robin-robin domain decomposition method for the Stokes-Darcy system. SIAM J. Numer. Anal. 49, 1064–1084 (2011)MathSciNetCrossRef
4.
Discacciati, M., Quarteroni, A., Valli, A.: Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. SIAM J. Numer. Anal. 45, 1246–1268 (2007)MathSciNetCrossRef
5.
6.
Du, G., Zuo, L.: Local and parallel finite element method for the mixed Navier-Stokes/Darcy model with Beavers-Joseph interface conditions. Acta Math. Sci. 37, 1331–1347 (2017)MathSciNetCrossRef
7.
Du, G., Hou, Y., Zuo, L.: A modified local and parallel finite element method for the mixed Stokes-Darcy model. J. Math. Anal Appl. 435, 1129–1145 (2016)MathSciNetCrossRef
8.
Du, G., Zuo, L.: A two-grid parallel partition of unity finite element scheme. Numer Algorithms. 80, 429–445 (2019)MathSciNetCrossRef
9.
Du, G., Zuo, L.: A Parallel Partition of Unity Scheme Based on Two-Grid Discretizations for the Navier-Stokes Problem. J. Sci. Comput. 75, 1445–1462 (2018)MathSciNetCrossRef
10.
Du, G., Zuo, L.: Local and parallel finite element post-processing scheme for the Stokes problem. Comput. Math. Appl. 73, 129–140 (2017)MathSciNetCrossRef
11.
He, Y., Xu, J., Zhou, A., Li, J.: Local and parallel finite element algorithms for the Stokes problem. Numer. Math. 109, 415–434 (2008)MathSciNetCrossRef
12.
He, Y., Xu, J., Zhou, A.: Local and parallel finite element algorithms for the Navier-Stokes problem. J. Comput. Math. 24, 227–238 (2006)MathSciNetMATH
13.
Hou, Y.: Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes-Darcy model. Appl. Math. Lett. 57, 90–96 (2016)MathSciNetCrossRef
14.
Hou, Y., Qin, Y.: On the solution of coupled Stokes/Darcy model with Beavers-Joseph interface condition. Comput. Math. Appl. 77, 50–65 (2019)MathSciNetCrossRef
15.
Larson, M., Målqvist, A.: Adaptive variational multi-scale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems. Comput. Methods Appl. Mech. Engrg. 196, 2313–2324 (2007)MathSciNetCrossRef
16.
Layton, W., Schieweck, F., Yotov, I.: Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40, 2195–2218 (2003)MathSciNetCrossRef
17.
Li, Y., Hou, Y.: Error estimates of a second-order decoupled scheme for the evolutionary Stokes-Darcy system. Appl. Numer. Math. 154, 129–148 (2020)MathSciNetCrossRef
18.
Li, R., Gao, Y., Yan, W, Chen, Z.: A Crank-Nicolson discontinuous finite volume element method for a coupled non-stationary Stokes-Darcy problem. J. Comput. Appl. Math. 353, 86–112 (2019)MathSciNetCrossRef
19.
Liu, Q., Hou, Y.: Local and parallel finite element algorithms for time-dependent convection-diffusion equations. Appl. Math. Mech. Engl. Ed. 30, 787–794 (2009)MathSciNetCrossRef
20.
Mu, M., Xu, J.: A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 45, 1801–1813 (2007)MathSciNetCrossRef
21.
Saffman, P.: On the boundary condition at the surface of a porous media. Stud. Appl. Math. 50, 93–101 (1971)CrossRef
22.
Song, L., Hou, Y., Zheng, H.: Adaptive local postprocessing finite element method for the Navier- Stokes equations. J. Sci. Comput. 55, 255–267 (2013)MathSciNetCrossRef
23.
Shan, L., Zheng, H.: Partitioned time stepping method for fully evolutionary Stokes-Darcy flow with the Beavers-Joseph interface conditions. SIAM J. Numer. Anal. 51, 813–839 (2013)MathSciNetCrossRef
24.
Shang, Y., Wang, K.: Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations. Numer. Algorithms. 54, 195–218 (2010)MathSciNetCrossRef
25.
Shang, Y., He, Y.: Parallel iterative finite element algorithms based on full domain partition for the stationary Navier-Stokes equations. Appl. Numer. Math. 60, 719–737 (2010)MathSciNetCrossRef
26.
Xu, J., Zhou, A.: Local and parallel finite element algorithms based on two-grid discretizations. Math. Comput. 69, 881–909 (1999)MathSciNetCrossRef
27.
Xu, J., Zhou, A.: Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Adv. Comput. Math. 14, 293–327 (2001)MathSciNetCrossRef
28.
29.
Zhang, Y., Hou, Y., Shan, L., Dong, X.: Local and parallel finite element algorithm for stationary incompressible magnetohydrodynamics. Numer. Meth. Part. D. E. 33, 1513–1539 (2017)MathSciNetCrossRef
30.
Zheng, H., Yu, J., Shi, F.: Local and parallel finite element method based on the partition of unity for incompressible flow. J. Sci. Comput. 65, 512–532 (2015)MathSciNetCrossRef
31.
Zheng, H., Shi, F., Hou, Y., et al.: and New local and parallel finite element algorithm based on the partition of unity. J. Math. Anal. Appl. 435, 1–19 (2016)MathSciNetCrossRef
32.
Zheng, H., Song, L., Hou, Y., et al.: The partition of unity parallel finite element algorithm. Adv. Comput. Math. 41, 937–951 (2015)MathSciNetCrossRef
33.
Yu, J., Shi, F., Zheng, H.: Local and parallel finite element algorithms based on the partition of unity for the Stokes problem. SIAM J. Sci. Comput. 36, C547–C567 (2014)MathSciNetCrossRef
34.
35.
Zuo, L., Du, G.: A multi-grid technique for coupling fluid flow with porous media flow. Comput. Math. Appl. 75, 4012–4021 (2018)MathSciNetCrossRef
36.
Zuo, L., Du, G.: A parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem. Numer. Algorithms. 77, 151–165 (2018)MathSciNetCrossRef
37.
Metadaten
Titel
Local and parallel finite element methods for the coupled Stokes/Darcy model
verfasst von
Guangzhi Du
Liyun Zuo
Publikationsdatum
19.10.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 4/2021
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-01021-5

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